The expression √(x² + (y - 1)²) - √(x² + (y + 1)²) = K describes a hyperbola when:

K lies in the interval (0, 2)
K lies in the interval (0, 1)
K lies in the interval (1, ∞)
K lies in the interval (0, ∞)

Correct answer: K lies in the interval (0, 2)

Solution

The expression describes a hyperbola when K lies in the interval (0, 2), which means the difference between the distances of any point on the hyperbola from the two foci is constant and equal to 2a.

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